The Resource Lyapunov exponents and smooth ergodic theory, Luis Barreira, Yakov B. Pesin

Lyapunov exponents and smooth ergodic theory, Luis Barreira, Yakov B. Pesin

Label
Lyapunov exponents and smooth ergodic theory
Title
Lyapunov exponents and smooth ergodic theory
Statement of responsibility
Luis Barreira, Yakov B. Pesin
Creator
Contributor
Subject
Language
eng
Summary
"This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows)." "The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory." "This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field."--Jacket
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1968-
http://library.link/vocab/creatorName
Barreira, Luis
Illustrations
illustrations
Index
index present
LC call number
QA611.5
LC item number
.B37 2002
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Pesin, Ya. B
Series statement
University lecture series,
Series volume
v. 23
http://library.link/vocab/subjectName
  • Ergodic theory
  • Lyapunov exponents
  • Dynamische systemen
  • Ergodiciteit
  • Théorie ergodique
  • Liapounov, Exposants de
  • Ergodic theory
  • Lyapunov exponents
  • Ergodiciteit
  • Dynamische systemen
  • Ergodentheorie
  • Ljapunov-Exponent
  • Ergodentheorie
  • Ljapunov-Exponent
Label
Lyapunov exponents and smooth ergodic theory, Luis Barreira, Yakov B. Pesin
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. 145-146) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ch. 1. Lyapunov Stability Theory of Differential Equations -- 1.1. Lyapunov Exponents for Differential Equations -- 1.2. Abstract Theory of Lyapunov Exponents -- 1.3. Forward and Backward Regularity -- 1.4. Stability Theory of Nonautonomous Differential Equations -- 1.5. Lyapunov Regularity and the Oseledets Decomposition -- Ch. 2. Elements of Nonuniform Hyperbolic Theory -- 2.1. Dynamical Systems with Nonzero Lyapunov Exponents -- 2.2. Nonuniform Hyperbolicity and Regular Sets -- 2.3. Holder Continuity of Invariant Distributions -- 2.4. Proof of the Multiplicative Ergodic Theorem -- Ch. 3. Examples of Nonuniformly Hyperbolic Systems -- 3.1. Anosov Diffeomorphisms -- 3.2. Diffeomorphisms with Nonzero Lyapunov Exponents on Surfaces -- 3.3. A Flow with Nonzero Lyapunov Exponents -- 3.4. Geodesic Flows on Compact Manifolds of Nonpositive Curvature -- Ch. 4. Local Manifold Theory -- 4.1. Existence of Local Stable Manifolds -- 4.2. Basic Properties of Stable and Unstable Manifolds -- 4.3. Absolute Continuity Property -- 4.4. Computing the Jacobian of the Holonomy Map -- 4.5. Partial Hyperbolicity -- Ch. 5. Ergodic Properties of Smooth Hyperbolic Measures -- 5.1. Absolute Continuity and Smooth Invariant Measures -- 5.2. Ergodicity of Smooth Hyperbolic Measures -- 5.3. Local Ergodicity -- 5.4. The Entropy Formula -- 5.5. SRB-Measures and General Hyperbolic Measures -- 5.6. Geodesic Flows on Compact Surfaces of Nonpositive Curvature
Dimensions
26 cm.
Extent
xii, 151 pages
Isbn
9780821829219
Lccn
2001045882
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)47838139
  • (OCoLC)ocm47838139
Label
Lyapunov exponents and smooth ergodic theory, Luis Barreira, Yakov B. Pesin
Publication
Bibliography note
Includes bibliographical references (p. 145-146) and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Ch. 1. Lyapunov Stability Theory of Differential Equations -- 1.1. Lyapunov Exponents for Differential Equations -- 1.2. Abstract Theory of Lyapunov Exponents -- 1.3. Forward and Backward Regularity -- 1.4. Stability Theory of Nonautonomous Differential Equations -- 1.5. Lyapunov Regularity and the Oseledets Decomposition -- Ch. 2. Elements of Nonuniform Hyperbolic Theory -- 2.1. Dynamical Systems with Nonzero Lyapunov Exponents -- 2.2. Nonuniform Hyperbolicity and Regular Sets -- 2.3. Holder Continuity of Invariant Distributions -- 2.4. Proof of the Multiplicative Ergodic Theorem -- Ch. 3. Examples of Nonuniformly Hyperbolic Systems -- 3.1. Anosov Diffeomorphisms -- 3.2. Diffeomorphisms with Nonzero Lyapunov Exponents on Surfaces -- 3.3. A Flow with Nonzero Lyapunov Exponents -- 3.4. Geodesic Flows on Compact Manifolds of Nonpositive Curvature -- Ch. 4. Local Manifold Theory -- 4.1. Existence of Local Stable Manifolds -- 4.2. Basic Properties of Stable and Unstable Manifolds -- 4.3. Absolute Continuity Property -- 4.4. Computing the Jacobian of the Holonomy Map -- 4.5. Partial Hyperbolicity -- Ch. 5. Ergodic Properties of Smooth Hyperbolic Measures -- 5.1. Absolute Continuity and Smooth Invariant Measures -- 5.2. Ergodicity of Smooth Hyperbolic Measures -- 5.3. Local Ergodicity -- 5.4. The Entropy Formula -- 5.5. SRB-Measures and General Hyperbolic Measures -- 5.6. Geodesic Flows on Compact Surfaces of Nonpositive Curvature
Dimensions
26 cm.
Extent
xii, 151 pages
Isbn
9780821829219
Lccn
2001045882
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
  • (OCoLC)47838139
  • (OCoLC)ocm47838139

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